dhsein(3P) Sun Performance Library dhsein(3P)NAMEdhsein - use inverse iteration to find specified right and/or left
eigenvectors of a real upper Hessenberg matrix H
SYNOPSIS
SUBROUTINE DHSEIN(SIDE, EIGSRC, INITV, SELECT, N, H, LDH, WR, WI, VL,
LDVL, VR, LDVR, MM, M, WORK, IFAILL, IFAILR, INFO)
CHARACTER * 1 SIDE, EIGSRC, INITV
INTEGER N, LDH, LDVL, LDVR, MM, M, INFO
INTEGER IFAILL(*), IFAILR(*)
LOGICAL SELECT(*)
DOUBLE PRECISION H(LDH,*), WR(*), WI(*), VL(LDVL,*), VR(LDVR,*),
WORK(*)
SUBROUTINE DHSEIN_64(SIDE, EIGSRC, INITV, SELECT, N, H, LDH, WR, WI,
VL, LDVL, VR, LDVR, MM, M, WORK, IFAILL, IFAILR, INFO)
CHARACTER * 1 SIDE, EIGSRC, INITV
INTEGER*8 N, LDH, LDVL, LDVR, MM, M, INFO
INTEGER*8 IFAILL(*), IFAILR(*)
LOGICAL*8 SELECT(*)
DOUBLE PRECISION H(LDH,*), WR(*), WI(*), VL(LDVL,*), VR(LDVR,*),
WORK(*)
F95 INTERFACE
SUBROUTINE HSEIN(SIDE, EIGSRC, INITV, SELECT, [N], H, [LDH], WR, WI,
VL, [LDVL], VR, [LDVR], MM, M, [WORK], IFAILL, IFAILR, [INFO])
CHARACTER(LEN=1) :: SIDE, EIGSRC, INITV
INTEGER :: N, LDH, LDVL, LDVR, MM, M, INFO
INTEGER, DIMENSION(:) :: IFAILL, IFAILR
LOGICAL, DIMENSION(:) :: SELECT
REAL(8), DIMENSION(:) :: WR, WI, WORK
REAL(8), DIMENSION(:,:) :: H, VL, VR
SUBROUTINE HSEIN_64(SIDE, EIGSRC, INITV, SELECT, [N], H, [LDH], WR,
WI, VL, [LDVL], VR, [LDVR], MM, M, [WORK], IFAILL, IFAILR, [INFO])
CHARACTER(LEN=1) :: SIDE, EIGSRC, INITV
INTEGER(8) :: N, LDH, LDVL, LDVR, MM, M, INFO
INTEGER(8), DIMENSION(:) :: IFAILL, IFAILR
LOGICAL(8), DIMENSION(:) :: SELECT
REAL(8), DIMENSION(:) :: WR, WI, WORK
REAL(8), DIMENSION(:,:) :: H, VL, VR
C INTERFACE
#include <sunperf.h>
void dhsein(char side, char eigsrc, char initv, int *select, int n,
double *h, int ldh, double *wr, double *wi, double *vl, int
ldvl, double *vr, int ldvr, int mm, int *m, int *ifaill, int
*ifailr, int *info);
void dhsein_64(char side, char eigsrc, char initv, long *select, long
n, double *h, long ldh, double *wr, double *wi, double *vl,
long ldvl, double *vr, long ldvr, long mm, long *m, long
*ifaill, long *ifailr, long *info);
PURPOSEdhsein uses inverse iteration to find specified right and/or left
eigenvectors of a real upper Hessenberg matrix H.
The right eigenvector x and the left eigenvector y of the matrix H cor‐
responding to an eigenvalue w are defined by:
H * x = w * x, y**h * H = w * y**h
where y**h denotes the conjugate transpose of the vector y.
ARGUMENTS
SIDE (input)
= 'R': compute right eigenvectors only;
= 'L': compute left eigenvectors only;
= 'B': compute both right and left eigenvectors.
EIGSRC (input)
Specifies the source of eigenvalues supplied in (WR,WI):
= 'Q': the eigenvalues were found using DHSEQR; thus, if H
has zero subdiagonal elements, and so is block-triangular,
then the j-th eigenvalue can be assumed to be an eigenvalue
of the block containing the j-th row/column. This property
allows DHSEIN to perform inverse iteration on just one diago‐
nal block. = 'N': no assumptions are made on the correspon‐
dence between eigenvalues and diagonal blocks. In this case,
DHSEIN must always perform inverse iteration using the whole
matrix H.
INITV (input)
= 'N': no initial vectors are supplied;
= 'U': user-supplied initial vectors are stored in the arrays
VL and/or VR.
SELECT (input/output)
Specifies the eigenvectors to be computed. To select the real
eigenvector corresponding to a real eigenvalue WR(j),
SELECT(j) must be set to .TRUE.. To select the complex eigen‐
vector corresponding to a complex eigenvalue (WR(j),WI(j)),
with complex conjugate (WR(j+1),WI(j+1)), either SELECT(j) or
SELECT(j+1) or both must be set to .TRUE.; then on exit
SELECT(j) is .TRUE. and SELECT(j+1) is .FALSE..
N (input) The order of the matrix H. N >= 0.
H (input) The upper Hessenberg matrix H.
LDH (input)
The leading dimension of the array H. LDH >= max(1,N).
WR (input/output)
On entry, the real and imaginary parts of the eigenvalues of
H; a complex conjugate pair of eigenvalues must be stored in
consecutive elements of WR and WI. On exit, WR may have been
altered since close eigenvalues are perturbed slightly in
searching for independent eigenvectors.
WI (input)
See the description of WR.
VL (input/output)
On entry, if INITV = 'U' and SIDE = 'L' or 'B', VL must con‐
tain starting vectors for the inverse iteration for the left
eigenvectors; the starting vector for each eigenvector must
be in the same column(s) in which the eigenvector will be
stored. On exit, if SIDE = 'L' or 'B', the left eigenvectors
specified by SELECT will be stored consecutively in the col‐
umns of VL, in the same order as their eigenvalues. A complex
eigenvector corresponding to a complex eigenvalue is stored
in two consecutive columns, the first holding the real part
and the second the imaginary part. If SIDE = 'R', VL is not
referenced.
LDVL (input)
The leading dimension of the array VL. LDVL >= max(1,N) if
SIDE = 'L' or 'B'; LDVL >= 1 otherwise.
VR (input/output)
On entry, if INITV = 'U' and SIDE = 'R' or 'B', VR must con‐
tain starting vectors for the inverse iteration for the right
eigenvectors; the starting vector for each eigenvector must
be in the same column(s) in which the eigenvector will be
stored. On exit, if SIDE = 'R' or 'B', the right eigenvec‐
tors specified by SELECT will be stored consecutively in the
columns of VR, in the same order as their eigenvalues. A com‐
plex eigenvector corresponding to a complex eigenvalue is
stored in two consecutive columns, the first holding the real
part and the second the imaginary part. If SIDE = 'L', VR is
not referenced.
LDVR (input)
The leading dimension of the array VR. LDVR >= max(1,N) if
SIDE = 'R' or 'B'; LDVR >= 1 otherwise.
MM (input)
The number of columns in the arrays VL and/or VR. MM >= M.
M (output)
The number of columns in the arrays VL and/or VR required to
store the eigenvectors; each selected real eigenvector occu‐
pies one column and each selected complex eigenvector occu‐
pies two columns.
WORK (workspace)
dimension((N+2)*N)
IFAILL (output) INTEGER array, dimension (MM)
If SIDE = 'L' or 'B', IFAILL(i) = j > 0 if the left eigenvec‐
tor in the i-th column of VL (corresponding to the eigenvalue
w(j)) failed to converge; IFAILL(i) = 0 if the eigenvector
converged satisfactorily. If the i-th and (i+1)th columns of
VL hold a complex eigenvector, then IFAILL(i) and IFAILL(i+1)
are set to the same value. If SIDE = 'R', IFAILL is not ref‐
erenced.
IFAILR (output) INTEGER array, dimension (MM)
If SIDE = 'R' or 'B', IFAILR(i) = j > 0 if the right eigen‐
vector in the i-th column of VR (corresponding to the eigen‐
value w(j)) failed to converge; IFAILR(i) = 0 if the eigen‐
vector converged satisfactorily. If the i-th and (i+1)th col‐
umns of VR hold a complex eigenvector, then IFAILR(i) and
IFAILR(i+1) are set to the same value. If SIDE = 'L', IFAILR
is not referenced.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, i is the number of eigenvectors which
failed to converge; see IFAILL and IFAILR for further
details.
FURTHER DETAILS
Each eigenvector is normalized so that the element of largest magnitude
has magnitude 1; here the magnitude of a complex number (x,y) is taken
to be |x|+|y|.
6 Mar 2009 dhsein(3P)
